Network Knowledge Graph (NKG)

• Network Knowledge Graph (NKG) is a formal structure that integrates network topology, element state, and relational semantics to support intent-based automation and advanced reasoning.
• NKG construction involves real-time telemetry ingestion, RDF triple-based and hyper-relational modeling, and validation using SHACL policies and simulated graph states.
• NKGs demonstrate scalability and efficient performance in telecom orchestration, achieving significant policy compliance and rapid validation times in large network simulations.

A Network Knowledge Graph (NKG) is a formal structure that integrates network topology, element state, and relational semantics into a unified, property-annotated graph, typically utilizing RDF-based serialization. NKGs underpin intent-based network orchestration, agentic automation, and advanced reasoning in domains such as autonomous 5G/6G networks and multi-party knowledge representation. They encode deterministic “ground truth” for network states and support the execution and verification of probabilistic or LLM-driven plans, representing a convergence of traditional network models and semantic knowledge graph constructs (Vijay et al., 23 Dec 2025, Batagelj et al., 1 May 2025).

1. Formal Schemas and Mathematical Foundations

NKGs generalize the network concept $N = (V, L, P, W)$—with node set $V$, link set $L$ (edges/arcs), node properties $P$, and link weights $W$—to accommodate arbitrary node and link properties and multi-relational semantics. In telecom automation, the NKG instantiates as a time-indexed directed graph $\mathcal{G}_t = (\mathcal{V}, \mathcal{E})$ where $\mathcal{V}$ ranges over standardized network functions (AMFFunction, UPFFunction, SMFFunction, AUSF, NSSF, NRF, gNB, etc. [3GPP TS 28.623]) and $\mathcal{E}$ aggregates interface and topological links annotated with interfaceType, timestamp, linkCapacity, and utilization. Each node $v \in \mathcal{V}$ encodes lastUpdated (xsd:dateTime), status $\in \{$ACTIVE, STANDBY, INACTIVE$\}$, and resource metrics. Edges $(v_i, v_j, \mathrm{type}, t, c)$ capture interface type, observation time, and capacity (Vijay et al., 23 Dec 2025).

For more abstract domain modeling, NKGs also adopt RDF triple-based representations where facts $(e_1, r, e_2)$ denote directed relations, and rich semantics are achieved by splitting nodes into simple nodes (entities) and triple-nodes (relations). Attributes can be realized either as literal-valued arcs or as node-level property functions (Batagelj et al., 1 May 2025).

2. Construction, Population, and Serialization

NKG population occurs via real-time telemetry ingestion—using gNMI, SNMP, NetConf protocols—into a staging database. Vendor-specific models are mapped to telecom standards (e.g., 3GPP class ontologies) through JSON-LD-based ontology alignment. Streaming ETL pipelines write updates to graph stores such as Neo4j (Enterprise v5), tagging mutations with timestamps and supporting historical queries (“Hypothetical Graph State” simulations) (Vijay et al., 23 Dec 2025). For general networks and multi-domain applications, Batagelj et al. propose an RDF “triple-node” format and detailed inductive construction rules: each RDF statement becomes a triple-node connected by arcs to subject and object simple nodes, yielding a bijective mapping between classical network structures and RDF graphs (Batagelj et al., 1 May 2025). Serializations in Turtle and JSON-LD encode all entities, predicates, and attributes using IRIs, blank nodes, or literals.

3. Policy Enforcement, Validation, and Verification Workflows

NKGs enable deterministic validation of network plans and LLM-generated actions. Before any plan execution, a subgraph $S_\text{sub}$ relevant to an intent $I$ is extracted via BFS limited by semantic tags. The plan is simulated on a copy of the current graph state $G_t$, and each mutation is subjected to SHACL shape constraints. Validation logic is expressed as

$$\mathrm{Verify}(a,\mathcal{G}) = \begin{cases} \mathrm{TRUE} & \text{if } \mathcal{G}' \models \mathcal{P} \land \mathrm{targets}(a) \subseteq \mathcal{V} \ \mathrm{FALSE} & \text{otherwise} \end{cases}$$

where $\mathcal{G}'$ is the simulated post-action graph, $\mathcal{P}$ is the set of SHACL policies, and $\mathrm{targets}(a)$ are action-referenced nodes. Safety violations, entity hallucinations (references to non-existent graph elements), and stale telemetry are rejected before orchestrator-level application (Vijay et al., 23 Dec 2025).

SHACL policies fall into four classes: topological constraints, resource limits, state invariants, and temporal freshness guardrails, embedded declaratively in the graph store. Sample shapes include “AMF cannot connect directly to UPF,” “slice bandwidth cannot exceed 100 Mbps,” and “telemetry too stale (>15s)” (Vijay et al., 23 Dec 2025).

4. N-ary and Hyper-relational Extensions

Beyond triple-based graphs, NKGs support n-ary fact representation for multi-entity events, transactions, and complex semantic couplings (Wei et al., 10 Jun 2025). The general hyper-relational formalization

$f = \bigl((h, r, t), \{(r_i: v_i)\}_{i=1}^q\bigr)$

or

$f = (r; e_1, \dots, e_n; a_1, \dots, a_m)$

permits joint modeling of entities, roles, and qualifiers (attributes). Such expressivity is necessary for domains requiring context, semantic unity, or multi-party interactions, such as financial records, scientific provenance, or 5G/6G multi-slice orchestration.

Link prediction in NKGs operates by ranking candidates for missing elements in n-ary facts using spatial (geometric embedding), tensor decomposition, or deep neural architectures (FCN, CNN, Transformers, GNNs). For example, in benchmark datasets (JF17K, WikiPeople, WD50K), neural network-based solutions notably outperform spatial and tensor methods, especially in scenarios with temporal, few-shot, or inductive challenges (Wei et al., 10 Jun 2025).

5. Embedding, Reasoning, and Intent Mapping

NKGs provide substrates for probabilistic reasoning and intent translation via knowledge graph embeddings (KGE). For intent-based networking, Gaussian-based embedding maps entity and relation nodes to multivariate normal distributions in $\mathbb{R}^d$. The composed distribution for a triple is $$p_{h,r} = \mathcal{N}(\mu_h + \mu_r, \Sigma_h + \Sigma_r)$$, scored against the target via KL-divergence:

$E(h,r,t) = D_{KL}(p_{h,r} \| q_t)$

Service prediction and intent validation tasks utilize embedding similarity—for instance, Mahalanobis distance between intended and candidate service embeddings. Closed-loop pipelines ensure that business intent is classified, validated for resource feasibility, translated to network API calls, and returned with assurance feedback. In telecom orchestration, embedding-based approaches yield top-1 service prediction accuracy of 84% and correct intent verification rates of 81% (Mehmood et al., 13 May 2024). Model retraining or incremental updating re-aligns reasoning as network telemetry evolves.

6. Performance, Scalability, and Analytical Applications

Empirical results indicate that NKG-based validation scales sublinearly with subgraph size $k$: $$L(k) \approx 142\,\mathrm{ms} \times (\frac{k}{12})^{1.2}$$, with practical overheads well below SMO-layer automation budget thresholds (e.g., $142 \pm 18\,\mathrm{ms}$ for $k \approx 12$ nodes; under $350\,\mathrm{ms}$ for $k \leq 50$ in synthetic 100K-node topologies) (Vijay et al., 23 Dec 2025). In comparative studies, NKG validation underpins most observed policy compliance and safety gains—68% versus 24% for SHACL policy corpus. The combined G-SPEC framework achieves remediation success rates of 94.1%, hallucination rates as low as 0.2%, and zero safety violations across hundreds of anomaly scenarios (Vijay et al., 23 Dec 2025).

NKGs also support classical network analysis. Once exported as adjacency matrices per predicate, one can compute centrality, structural clustering, modularity, co-authorship, and temporal event relations using standard graph-theoretic methods (Batagelj et al., 1 May 2025). Storing all representations in RDF, augmented with domain ontologies, ensures FAIR data interoperability and easy integration with analytic ecosystems (SPARQL, Pajek, Python).

7. Use Cases, Limitations, and Future Directions

NKGs have been deployed in domains including 5G/6G core orchestration, bibliographic analytics, event networks, biomedicine, and finance (Vijay et al., 23 Dec 2025, Batagelj et al., 1 May 2025, Wei et al., 10 Jun 2025). They support safe agentic automation, closed-loop intent realization, multi-party fact inference, and semantic interoperability.

Limitations include lack of explicit temporal reasoning in basic KGE models, sensitivity to negative sampling, and potential scalability barriers with web-scale graphs. Future work encompasses dynamic and temporal embedding schemes (TTransE, HyTE), reinforcement learning integration for arbitration, explainability drives (counterfactual and causal analyses), and cross-modal entity fusion (textual, numeric, structural) (Wei et al., 10 Jun 2025, Mehmood et al., 13 May 2024). A plausible implication is that LLM-based NKG completion, real-time adaptation, and enhanced policy reasoning will further consolidate the role of NKGs in autonomous, safe, and intent-assured networks.